1) On the application, it said that medical examination can be submitted up front. How does that work? If we do the medicals ahead of time, we won't have case number of anything to submit them with.
You are applying inland, so medicals have to be done in advance and proof of that has to be included in your application (take a look at the document checklist). There is a form - Medical report, to be exact - that your fiancee will fill out and take with her to the DMP (designated medical practitioner), and the DMP's office will then send that form to their regional medical centre. CIC will request medical results from the regional centre not from you.
2) She is currently employed, and will be applying for the extension to the work permit. But if her permit and SIN expire before the decision is made, can she still continue to work for her existing employee? Can she seek employment with other companies?
She can continue to work with her current employer on implied status; if she wanted to change companies she would have to get a new LMO and a new work permit.
3) Does it have any benefit to apply for work permit extension together with the PR application? PR application has to be done via mail, but the processing times for work permit extension online seem to be faster.
As a member of Spouse/Common law Partner in Canada class, after 1st stage approval (or AIP, approval in principle) she would be eligible for an open work permit, which would make it possible for her to work for any employer - but to get it, she would have to send extension/change of status form together with the PR application, to make Vegreville aware of the situation. Until the end of 1st stage processing (currently it takes 9-10 months) she could keep working for her current employer under implied status.
[4) We've read about the "implied status" while the application is being processed. But during that time, what is her proof of legal status in Canada? Any document or note from CIC?
You would need proof that she applied for extension/change of status - copy of the receipt showing $150 processing fee for the application and a confirmation from whichever delivery service you use should do.
5) Her passport will expire next Autumn, before the expected result from the PR application. The embassy will not renew the passport unless it has less than 6 months left. In either case, she will change her passport midway through the application. Changed passport will have different passport number. How does that affect the application? How would we add that to the application?
When CIC starts processing your application you will receive your file number in the mail. You can then use this number to have any set of additional documents you send to Vegreville matched with the original application. (They even give you stickers with your number, so neat

)
6) After getting married, she will assume my last name (which is different from legally changing her last name, but she will change the name of driver's license, bank cards, etc). In the PR application, there are 2 similar question where last name is required:
(...) Should this include the assumed name from marriage?
Is she going to be applying under her maiden name? Keep in mind that in that case her PR card will be issued in that name; it's possible to change it later, but that will take some time and money.
In any case, if she's going to have certain documents in her assumed name, then yes, include that name in the questions you mentioned (and explain it's her assumed name).
Hope this helps
